Topology Geometry And Field Theory
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Topology Geometry And Quantum Field Theory
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Author : Ulrike Luise Tillmann
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-28
Topology Geometry And Quantum Field Theory written by Ulrike Luise Tillmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-28 with Mathematics categories.
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.
Quantum Field Theory And Topology
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Author : Albert S. Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-10-21
Quantum Field Theory And Topology written by Albert S. Schwarz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-21 with Mathematics categories.
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Mathematics categories.
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Conformal Field Theory And Topology
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Author : Toshitake Kohno
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Conformal Field Theory And Topology written by Toshitake Kohno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Translated from the Japanese, this brief monograph offers an introduction to the geometric aspects of conformal field theory and its application to topological variants. It begins with a description based on loop groups, and proceeds to define topological invariants for knots and 3-manifolds. A brief discussion of Chern- Simons permutation theory also appears. Diagrams illustrate key points. Khono's credentials are not listed. Annotation copyrighted by Book News, Inc., Portland, OR.
Differential Topology And Quantum Field Theory
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Author : Charles Nash
language : en
Publisher:
Release Date : 1991
Differential Topology And Quantum Field Theory written by Charles Nash and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool on quantum field theory are presented in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following on from his previous work, covers elliptic differential and pseudo-differential operators, Atiyah-Singer Index theory, Morse theory, instantons and monopoles, topological quantim field theory, string theory and knot theory.The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. -- from back cover
Topological Field Theory Primitive Forms And Related Topics
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Author : A. Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Field Theory Primitive Forms And Related Topics written by A. Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Topology And Geometry In Physics
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Author : Eike Bick
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-18
Topology And Geometry In Physics written by Eike Bick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-18 with Mathematics categories.
Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.
Twistor Geometry And Field Theory
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Author : R. S. Ward
language : en
Publisher: Cambridge University Press
Release Date : 1990
Twistor Geometry And Field Theory written by R. S. Ward and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Geometry Topology And Physics
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Author : Mikio Nakahara
language : en
Publisher: Taylor & Francis
Release Date : 2018-10-03
Geometry Topology And Physics written by Mikio Nakahara and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Topology Geometry And Field Theory
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Author :
language : en
Publisher:
Release Date : 1994
Topology Geometry And Field Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with MATHEMATICS categories.